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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">U1</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U1</font>, <font color="Maroon">B</font> be   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U1</font>;<br/>





<b>assume </b><a NAME="E1:20"/>
<font color="Maroon">A</font> is    <a href="pboole.html#M4">ManySortedSubset</a> of <font color="Maroon">B</font>
 ;<br/>

<a NAME="E2:20"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">A</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E3:20"/>
<font color="Maroon">B</font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D18">MSUALG_2:def 18</a></i>;<br/>
<a NAME="E4:20"/><b>then </b>
<font color="Maroon">B</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E5:20"/><b>then </b>
<font color="Maroon">A</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>
<a NAME="E6:20"/><b>then </b>
<font color="Maroon">A</font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<b>hence </b><a NAME="E7:20"/>
 <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">A</font> is    <a href="msualg_2.html#M1">MSSubAlgebra</a> of  <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="msualg_2.html#D18">MSUALG_2:def 18</a></i>;<br/>


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